EP2260556B1 - Method and arrangement for generating an error signal - Google Patents

Description

The invention relates to an arrangement and a method for generating an error signal, which characterizes the location of a ground fault on a line between two line ends, wherein in the method at both line ends in each case the voltage and the current are measured to form measured values and after or at a detection of an earth fault, the location of the ground fault is determined. With such a method, for example, ground faults in networks with isolated neutral point or with resonance neutral point grounding can be detected and located.

Earth faults in networks with isolated neutral point or with resonance earthing lead to a voltage increase in the entire transformer network decoupled subnet. The localization of ground faults always causes difficulties and leads to time-consuming search circuits, since the methods used to date for detecting earth faults are not always selective.

Previous methods use devices that use the principle of Wattmetric earth fault detection, harmonics or ground-fault wiper relays for ground fault detection.

Devices based on the principle of Wattmetric earth fault detection determine the complex pointers of the zero system variables of current and voltage of the fundamental oscillation. From these variables, the active and reactive power of the zero system variables is determined. The active component of this signal indicates the direction to the earth fault as seen from the relay installation point. The determined Directional signals must be transported via telecontrol or control technology from the devices to a central evaluation point. There, the line affected by the ground fault can be determined by means of manual or program-supported evaluation. The principle of Wattmetric earth fault detection requires very accurate transducers with small angle errors. Usually used cable conversion converters must be adjusted during commissioning in order to meet the high accuracy requirements of the process. Since the angular errors of the transducers to be corrected depend on the modulation of the transducers, this calibration is prone to error and can lead to unreliable displays.

The following two variants are known in the principle of the earth-fault wiper relay: In the first variant, the sign of the first half-cycle of the transient transient of the ground fault is evaluated. However, this first variant only works if there is a sudden ground fault, if possible in the voltage maximum. In the second variant, also called qu-method, the displacement current is calculated from the instantaneous values of the voltage and the zero capacitance of the line to be examined, and a Lissajou figure is formed with the measured zero current. The rise of this curve allows a determination of the earth fault direction.

In the case of the harmonic oscillation method, harmonics are impressed artificially via a transformer star point and these impressed harmonics are utilized for the earth fault detection. Due to the active supply of the harmonics, additional primary technology is necessary in the network. The method allows only the determination of the earth fault direction.

Furthermore, from the EP 0 933 643 A1 a method for locating a fault in a three-phase network, in which with the aid of detected at two measuring points zero system currents and voltages a faulty node in the three-phase network can be determined.

The invention has for its object to provide a reliable method for Erdschlussortung.

This object is achieved by a method having the features according to claim 1. Advantageous embodiments of the method according to the invention are specified in subclaims.

Thereafter, the invention provides that is determined with the measured values contained in the zero voltage or zero current harmonic content and its time decay constant for each of the two line ends, with the harmonic component and the decay constant for each line end each a harmonic generator measured magnitude and phase is formed, wherein the temporal reference point of the phase of the harmonic generator measured value relates to the time of ground fault detection at the respective line end, the harmonic generator measured in this way are rotated from their respective end of the line in time to the past and determined at what time in the past and at what point on the line, the reverted harmonic generator readings are at least approximately equal in magnitude and at least approximately the same phase, and the location thus determined is al s location of the ground fault is considered and output with the error signal.

A significant advantage of the method according to the invention is the fact that these harmonics are evaluated, whereby a very accurate fault location is possible. Also, only small demands on the measurement accuracy of the converter used must be made, since the location of a ground fault in the method according to the invention can be determined very accurately even with not specially matched transducers.

Another significant advantage of the method according to the invention is the fact that this method - in contrast to the previously described prior art method - works reliably even in so-called ground fault wipers. The location of the ground fault wiper does not always work reliably with previously known methods, since ground-fault wipers are only transiently present.

A third significant advantage of the method according to the invention is that the measurement of the voltage at the two line ends can take place without synchronization and the voltage measurement values at the two line ends can be unsynchronized.

According to a preferred embodiment of the method, it is provided that, taking into account the telegraph equation describing the propagation of electromagnetic waves on lines for a selectable location on the line, a first and a second zero voltage pointer for a time past the propagation time to the selectable location using the Harmonic generator magnitudes of zero current and zero voltage at the two line ends are calculated, the first zero voltage pointer being calculated from the first line end towards the second line end and the second zero voltage pointer from the second line end towards the first line end, the two zero voltage pointers calculated in this way are compared with each other and the one place is selected where the calculated zero voltage pointers best match, and the line location determined in this way as the location of the Earth fault is considered. With the telegraph equation locating is very easy and fast possible.

According to a further preferred embodiment of the method, it is provided that the two harmonic generator measured quantities are determined by magnitude and phase in each case on the basis of a predetermined signal model, which simulates the time course of the zero voltage in the case of a ground fault, by means of an estimation method, wherein the predetermined signal model at least the Determining harmonic generator measuring variable with a fixed pointer circle frequency, the determined time decay constant of the harmonic component and a Nullspannungszeigermessgröße with the fundamental frequency of the zero voltage and wherein the amount and the phase of the harmonic generator measured variable are adjusted in the estimation method such that the deviation between the temporal waveform of the simulated signal of Signal model and the measured temporal waveform of the measured values of the zero voltage is minimal. As an estimation method, a least-squares estimation method, a Kalman filter algorithm or an ARMAX estimation method is preferably used.

Moreover, it is considered advantageous if a frequency dominant for the harmonic component is selected from the frequency spectrum of the harmonic component and the pointer frequency of the harmonic generator parameters is in each case set such that it corresponds to the dominant frequency. For example, in the harmonic content that harmonic frequency can be determined whose amplitude is maximum, and these are set as the pointer circle frequency.

The time window for the data used to determine the harmonic generator measurement values is preferably determined such that the time window beginning at the beginning of the rise of the zero voltage is set after exceeding a predetermined threshold.

The harmonic content is preferably determined by opening a measurement window for each line end after detection of the ground fault, for which the frequency spectrum of the zero voltage is determined by means of a Fourier transformation, and the frequency spectrum is subjected to high-pass filtering, in which the harmonics of the fundamental frequency of the zero voltage be separated by forming the harmonic component.

The decay constant can be determined particularly simply and thus advantageously by determining the rms value of the harmonic component and determining the time decay constant of the rms value and determining the determined time decay constant of the rms value as the time decay constant of the harmonic component.

In order to achieve the lowest possible expenditure on equipment, it is considered advantageous if, in the method, the measurement of voltage and current takes place without synchronization at the two line ends and the voltage and current measured values at the two line ends are unsynchronized.

The invention also relates to an arrangement for generating an error signal characterizing the location of a ground fault on a line between a first and a second line end, the arrangement comprising: a first measuring device at the first line end of the line and a second measuring device at the line second line end of the line.

According to the invention, an evaluation device connected to the two measuring devices is provided, which is suitable for carrying out a method with the measured values of the two measuring devices, as described above.

The evaluation device can be formed for example by a programmed data processing system.

The evaluation device can be arranged in a central device with which the two measuring devices are connected. Alternatively, the two measuring devices can be connected to one another, wherein the evaluation device is implemented in one of the measuring devices.

The invention also relates to a field device, in particular protective device, for connection to a line end of an electrical line and for detecting a ground fault on the line. According to the invention, the field device comprises: an evaluation device which is suitable for carrying out a method as described above, and a data connection for connection to another measuring device for receiving measured values relating to the other line end of the line.

Figur 1

eine Anordnung mit drei Feldgeräten,

Figur 2

das elektrische Ersatzschaltbild der Anordnung gemäß Figur 1,

Figuren 3, 4

vereinfachte elektrische Ersatzschaltbilder der Anordnung gemäß Figur 1,

Figur 5

ein elektrisches Ersatzschaltbild einer erdschlussbehafteten Energieübertragungsleitung,

Figur 6

einen typischen Verlauf der Nullgrößen bei einem Erdschluss,

Figur 7

Signalverarbeitungsschritte zur Datenfenster- und Zeitkonstantenbestimmung,

Figur 8

Spektren von Nullstrom und Nullspannung,

Figur 9

die Übereinstimmung von gemessenen und geschätzten Signalen (komplettes Datenfenster),

Figur 10

die Übereinstimmung von gemessenen und geschätzten Signalen (Ausschnitt),

Figur 11

berechnete komplexe Zeiger,

Figur 12

den Verlauf einer Kostenfunktion,

Figur 13

schematisch die Ausbreitung einer Welle auf einer Leitung und

Figur 14

ein Ausführungsbeispiel für ein erfindungsgemäßes Feldgerät.

The invention will be explained in more detail with reference to embodiments; thereby show exemplarily:

FIG. 1

an arrangement with three field devices,

FIG. 2

the electrical equivalent circuit diagram of the arrangement according to FIG. 1 .

FIGS. 3, 4

simplified electrical equivalent circuit diagrams of the arrangement according to FIG. 1 .

FIG. 5

an electrical equivalent circuit diagram of a faulty power transmission line,

FIG. 6

a typical course of the zero values in case of a ground fault,

FIG. 7

Signal processing steps for data window and time constant determination,

FIG. 8

Spectra of zero current and zero voltage,

FIG. 9

the match of measured and estimated signals (complete data window),

FIG. 10

the agreement of measured and estimated signals (detail),

FIG. 11

calculated complex pointers,

FIG. 12

the course of a cost function,

FIG. 13

schematically the propagation of a wave on a pipe and

FIG. 14

an embodiment of an inventive field device.

For the sake of clarity, the same reference numbers are always used in the figures for identical or comparable components.

In the FIG. 1 an electrical arrangement is shown comprising three substations 10, 20 and 30. In the substation 10, two field devices 40 and 41 are included, in the two substations 20 and 30 each one. The four field devices 40, 41, 42 and 43 may be identical, for example, but this is not mandatory.

The junction A of the substation 10 and the junction B of the substation 20 are connected to each other by an example, three-phase power transmission line 50; the junction A of the substation 10 and the junction C of the substation 30 are connected together by an example, three-phase power transmission line 60.

The field devices are connected via their data connection D40, D41, D42 and D43 to local networks 70, routers 80 and a WAN 90 (WAN: wide area network), such as the Internet, and thus also to each other in a data connection, for example to the ETHERNET Standard using fixed IP addresses for each of the field devices.

By way of example, the field device 40 of the substation 10 can exchange data with the field device 42 of the substation 30 via this data connection, for example the measured values of current and voltage at the respective connection points A and C and / or measured values derived therefrom, such as harmonic vector measured quantities in magnitude and phase , For example, harmonic generator readings U0A and I0A may be transmitted from the field device 40 to the field device 42 and harmonic generator readings U0C and I0C from the field device 42 to the field device 40.

The simplified electrical equivalent circuit diagram of the arrangement according to the FIG. 1 show by way of example the FIGS. 2 and 3 , It can be seen that the subnetwork to the right of a transformer 100 of the substation 10 is provided with a resonance neutral point earthing. If an equivalent resistance and an equivalent voltage source are formed in this subsystem for the positive sequence and negative sequence system, a simplified equivalent circuit diagram is created FIG. 4 is shown.

In the FIG. 14 an embodiment of the field device 42 is shown. The field devices 40, 41 and 43 are off FIG. 1 can be identical or similar.

One recognizes in the FIG. 14 a zero voltage generator 120 and a zero-current generator 125, which are connected on the input side to the junction C of the substation 30 and current readings Mi and voltage readings Mu obtained. Downstream of the zero-voltage generator 120 and the zero-current generator 125 are a device 130 for determining a decay constant τ, a device 135 for determining a harmonic frequency fm and an estimator 140.

The means 130 for determining the decay constant τ comprises a high pass 145, an effective value generator 150 and a time constant determiner 155.

The device 135 for determining the harmonic frequency fm comprises an FFT device (FFT: Fast Fourier Transformation) 160 and a maximum value searcher 165.

The outputs of the devices 130 and 135 are connected to other inputs of the estimator 140. On the output side, the estimation device 140 is provided with a fault locating device 170 in connection, the input side is also connected to the data port D42.

• Zunächst bilden der Nullspannungsbildner 120 sowie der Nullstrombildner 125 Nullspannungswerte und Nullstromwerte.

The field device 42 can be operated, for example, as follows:

• First, the zero voltage generator 120 and the zero current generator 125 form zero voltage values and zero current values.

The means 130 for determining the decay constant filters out the harmonic component with its high-pass 145 from the zero voltage and, together with the rms value generator 150, forms an effective value of the harmonic component. With the time course of the rms value of the harmonic content, the time constant determiner 155 determines the time drop of the rms value to form the decay constant τ which reaches the estimator 140.

The maximum value finder 165 of the device 135 retrieves a dominating frequency fm in the voltage frequency spectrum formed by the FFT device 160 and sends it to the estimator 140. For example, the maximum value finder 165 in the harmonic content will determine the harmonic frequency whose amplitude is maximum and this frequency spend as dominating frequency fm.

In the estimator 140, a signal model is stored, which simulates the time course of the zero voltage in the event of a ground fault. The signal model takes into account as influencing parameters determining the signal progression a harmonic generator measuring variable with the dominant frequency fm, the decay constant τ and a zero voltage indicator measured value the fundamental frequency of the zero voltage. According to a predetermined estimation method, the estimation means 140 adjusts the amount and phase of the harmonic generator measured value by using this signal model until the deviation between the temporal waveform of the simulated signal of the signal model and the measured temporal waveform of the measured values of the zero voltage is minimum. In this way, on the output side with the harmonic component and the decay constant τ a harmonic generator measured magnitude and phase for the voltage and correspondingly formed for the current, wherein the time reference point of the phase of the harmonic generator measurement refers to the time of ground fault detection at the respective line end. The harmonic current measurement quantities for current and voltage are identified by the reference symbols U0C and I0C.

The harmonic generator measuring quantities U0C and I0C as well as the harmonic current measuring quantities U0A and I0A reach the fault locating device 170, which chronologically rotates and determines the harmonic generator measured quantities formed in the manner described from their respective line end A or C, at which point in time in the past and at which point on the line 60 the two back-rotated harmonic measures U0C and U0A and the two back-rotated harmonic readings I0A and I0C have at least approximately the same amount and at least approximately the same phase. The location determined in this way is regarded as the location of the ground fault and output with the error signal F.

The mathematical turning back of the harmonic generator magnitudes can be described, for example, taking into account the propagation of electromagnetic waves on lines Telegraph equation. Here, for a selectable location, the magnitude and phase of the harmonic generator measurement value of the zero voltage for a time lying around the propagation time to the selectable location in the past is calculated from the harmonic generator magnitudes of zero current and zero voltage of its own line end toward the other line end. The zero voltage hands calculated in this way - starting from each of the two conductor ends - are compared with each other and the location where the calculated hands best match is selected.

The components 120, 125, 130, 135, 140 and 170 of the field device 42 form an evaluation device 200; this can be formed for example by a data processing system.

• Wenn davon ausgegangen wird, dass die Messwerte von Nullsystemspannung und Nullsystemstrom für die Netzknoten A und C zur Verfügung stehen, kann für eine fehlerbehaftete Leitung ein Ersatzschaltbild des Nullsystems aufgestellt werden, wie es in der Figur 5 dargestellt ist.

For example, the procedure for determining the fault location described above may be as follows in detail:

• If it is assumed that the measured values of zero system voltage and zero system current are available for the network nodes A and C, an equivalent circuit diagram of the zero system can be set up for a faulty line, as described in US Pat FIG. 5 is shown.

mit : $$K=\left(\begin{array}{cc}\cosh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)& Z_W\left(\mathit{j\omega }\right)\cdot \sinh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)\\ \frac{1}{Z_W\left(\mathit{j\omega }\right)}\cdot \sinh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)& \cosh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)\end{array}\right)$$

und : $$Z_W\left(\mathit{j\omega }\right)=\sqrt{\frac{\mathit{Rʹ}+\mathit{i\omega }\cdot \mathit{Lʹ}}{\mathit{Gʹ}+\mathit{i\omega }\cdot \mathit{Cʹ}}}$$

$$\gamma \left(\mathit{j\omega }\right)=\sqrt{\left(\mathit{Rʹ}+\mathit{i\omega }\cdot \mathit{Lʹ}\right)\cdot \left(\mathit{Gʹ}+\mathit{i\omega }\cdot \mathit{Cʹ}\right)}$$

In the FIG. 5 two loops are to be recognized, which contain a common voltage at the fault point F for the voltage in the zero system at the fault point U0F. The two four-poles KA and KC represent the line model of the zero system from the line ends of the nodes A and C to the error point F. The following equation shows the chain matrix for the four poles: $$\left(\begin{array}{c}{U}_2\\ I_2\end{array}\right)=\left(\begin{array}{cc}{k}_{11}& k_{12}\\ k_{21}& k_{22}\end{array}\right)\cdot \left(\begin{array}{c}{U}_1\\ {\mathrm{<figure-callout\; id="1"\; label="I"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">I</figure-callout>}}_1\end{array}\right)$$

with : $$K=\left(\begin{array}{cc}\cosh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)& Z_W\left(\mathit{j\omega }\right)\cdot \sinh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)\\ \frac{1}{Z_W\left(\mathit{j\omega }\right)}\cdot \sinh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)& \cosh \left(\gamma \left(\mathit{j\omega }\right)\cdot l\right)\end{array}\right)$$

and : $$Z_W\left(\mathit{j\omega }\right)=\sqrt{\frac{\mathit{R\; \text{'}}+\mathit{i\omega }\cdot \mathit{L\text{'}}}{\mathit{G}+\mathit{i\omega }\cdot \mathit{C\; \text{'}}}}$$

$$\gamma \left(\mathit{j\omega }\right)=\sqrt{\left(\mathit{R\; \text{'}}+\mathit{i\omega }\cdot \mathit{L\text{'}}\right)\cdot \left(\mathit{G}+\mathit{i\omega }\cdot \mathit{C\; \text{'}}\right)}$$

mit $$U_{0\mathit{F}}=U_{0\mathit{rA}}=k_{11}\left(\mathit{j\omega },l\right)\cdot U_{0\mathit{A}}+k_{12}\left(\mathit{j\omega },l\right)\cdot I_{0A}$$

$$U_{0\mathit{F}}=U_{0\mathit{rC}}=k_{11}\left(\mathit{j\omega },1-l\right)\cdot U_{0\mathit{C}}+k_{12}\left(\mathit{j\omega },1-l\right)\cdot I_{0C}$$

The quantities R ', L', G 'and C' represent the kilometric quantities of series resistance, series inductance, parallel conductance and parallel capacitance of the line. The following two equations can now be set up for the error location: $${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rC}}={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0F}$$

With $${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{F}}={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}=k_{11}\left(\mathit{j\omega },l\right)\cdot {\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{A}}+k_{12}\left(\mathit{j\omega },l\right)\cdot I_{0A}$$

$${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{F}}={\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rC}}=k_{11}\left(\mathit{j\omega }.1-\mathrm{<figure-callout\; id="0"\; label="l\; \cdot \; U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">l\; </figure-callout>}\right)\cdot U_{}{}_{0\mathit{C}}+k_{12}\left(\mathit{j\omega }.1-l\right)\cdot I_{0C}$$

The functions k as a function of the frequency for a given line length can be assumed to be known. This leaves only the error distance l as an unknown quantity for the system of equations set up above. This size can be determined by directly solving the given equation when the complex pointers are for U0A, I0A, U0C, and I0C.

mit $$U_{0\mathit{rF}}=k_{11}\left(\mathit{j\omega },l\right)\cdot U_{0\mathit{A}}+k_{12}\left(\mathit{j\omega },l\right)\cdot I_{0A}$$

$$U_{0\mathit{rC}}=k_{11}\left(\mathit{j\omega },1-l\right)\cdot U_{0\mathit{C}}+k_{12}\left(\mathit{j\omega },1-l\right)\cdot I_{0C}$$

By setting up a cost function, the above function can be transformed into a nonlinear optimization problem. In this case, in addition, the parameters of the kilometric impedances can be included in the vector of the quantities to be optimized. As a cost function the square model error of the voltage at the fault location can be used: $$e\left(l,\mathit{j\omega },\mathit{R\; \text{'}},\mathit{L\text{'}},\mathit{G},\mathit{C\; \text{'}}\right)={\left(\mathrm{re}\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}\right\}-\mathrm{<figure-callout\; id="0"\; label="re\; U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">re\; </figure-callout>}\left\{U_{}\right\}\left\{{}_{0\mathit{<figure-callout\; id="2"\; label="rC"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">rC</figure-callout>}}\right\}\right)}^2+{\left(\mathrm{in\; the}\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}\right\}-\mathrm{in\; the}\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{<figure-callout\; id="2"\; label="rC"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">rC</figure-callout>}}\right\}\right)}^2$$

With $${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rh}}=k_{11}\left(\mathit{j\omega },l\right)\cdot {\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{A}}+k_{12}\left(\mathit{j\omega },l\right)\cdot I_{0A}$$

$${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rC}}=k_{11}\left(\mathit{j\omega }.1-\mathrm{<figure-callout\; id="0"\; label="l\; \cdot \; U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">l\; </figure-callout>}\right)\cdot U_{}{}_{0\mathit{C}}+k_{12}\left(\mathit{j\omega }.1-l\right)\cdot I_{0C}$$

mit $$l\in \left[01\right]$$

By applying an example from the scripture " A Fast Algorithm For Fast Nonlinearly Constrained Optimization Calculations "(Powell, MJD, Numerical Analysis, GA Watson ed., Lecture Notes in Mathematics, Springer Verlag, Vol. 630, 1978 ) known nonlinear optimization method, the following optimization task is solved: $$\underset{l}{\min }e\left(l,\mathit{j\omega },\mathit{R\; \text{'}},\mathit{L\text{'}},\mathit{G},\mathit{C\; \text{'}}\right)$$

With $$l\in \left[01\right]$$

For the complex pointers U0A, I0A, U0C and I0C not the pointers of the fundamental wave are used, but pointers for the dominant transient frequency. These can be determined, for example, as follows: In the zero system, the reactance of the Petersen coil located in the neutral point of the feed transformer and the capacitance of the overall network to ground produces a parallel resonant circuit which is tuned to the mains frequency. This signal provides a good balance with a correlated proportion to the fundamental wave pointer and can thus cause significant measurement errors in the pointer determination. However, the longitudinal inductances of the network form, with the earth capacitances of the line, further series and parallel resonant circuits which, in the case of ground fault, discharge by discharging the conductor affected by the ground fault and charging it the unaffected conductors are excited to transient phenomena at their natural frequency.

The FIG. 6 shows a typical course of zero current and voltage at a Erdschlusseintritt. In the FIG. 6 clearly shows the transient of the zero voltage (upper diagram) and the zero current (lower diagram). Here it can be seen that the amplitude of the zero current during the transient is a multiple of the current amplitude during the steady state.

The FIG. 7 shows a section of the transient of the voltage; where u0 is the measured zero voltage, u0eff is the rms value of the zero voltage, u0hp is the high-pass filtered zero voltage, and u0eff-hp is the high-pass filtered rms value of the zero voltage.

$$T_C=\mathrm{Im}\left\{\gamma \right\}\cdot \left(1-l\right)$$

To determine the start of the data window, for example, the exceeding of a U0 threshold value is used as the starting value. For example, to synchronize the data windows from both ends of the line, pre-fault sizes may be used in conjunction with a healthy-line null-system model. Alternatively, the time difference of the data windows can be included in the solution of the nonlinear optimization. For this purpose, the propagation times of the wave from the point of failure to the measuring locations, for example, are considered as follows (cf. FIG. 13 ): With the aid of the propagation time constant of the telegraph equation, the distance of the measuring locations from the fault location to a transit time of the wave from fault location to the measuring locations can be converted: $$T_A=\mathrm{in\; the}\left\{\gamma \right\}\cdot l$$

$$T_C=\mathrm{in\; the}\left\{\gamma \right\}\cdot \left(1-l\right)$$

mit $$U_{0\mathit{rA}}=k_{11}\left(\mathit{j\omega },l\right)\cdot U_{0\mathit{A}}\cdot e^{-j\mathrm{Im}\left\{\gamma \right\}\cdot l}+k_{12}\left(\mathit{j\omega },l\right)\cdot I_{0A}\cdot e^{-j\mathrm{Im}\left\{\gamma \right\}\cdot l}$$

$$U_{0\mathit{rC}}=k_{11}\left(\mathit{j\omega },1-l\right)\cdot U_{0\mathit{C}}\cdot e^{-j\mathrm{Im}\left\{\gamma \right\}\cdot \left(1-l\right)}+k_{12}\left(\mathit{j\omega },1-l\right)\cdot I_{0C}\cdot e^{-j\mathrm{Im}\left\{\gamma \right\}\cdot \left(1-l\right)}$$

If the times of the arrival of the wave at the measuring locations are now determined exactly from the starting point of the zero voltage, the time offset of these times with respect to the error entry time at the measuring point A can be indicated by TA and at the measuring point C by TC. These time shifts can now be considered in the approach as follows: $$e\left(l,\mathit{j\omega },\mathit{R\; \text{'}},\mathit{L\text{'}},\mathit{G},\mathit{C\; \text{'}}\right)={\left(\mathrm{re}\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}\right\}-\mathrm{<figure-callout\; id="0"\; label="re\; U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">re\; </figure-callout>}\left\{U_{}\right\}\left\{{}_{0\mathit{<figure-callout\; id="2"\; label="rC"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">rC</figure-callout>}}\right\}\right)}^2+{\left(\mathrm{in\; the}\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}\right\}-\mathrm{in\; the}\left\{{\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{<figure-callout\; id="2"\; label="rC"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">rC</figure-callout>}}\right\}\right)}^2$$

With $${\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{rA}}=k_{11}\left(\mathit{j\omega },l\right)\cdot {\mathrm{<figure-callout\; id="0"\; label="U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">U</figure-callout>}}_{0\mathit{A}}\cdot e^{-j\mathrm{in\; the}\left\{\gamma \right\}\cdot l}+k_{12}\left(\mathit{j\omega },l\right)\cdot I_{0A}\cdot e^{-j\mathrm{in\; the}\left\{\gamma \right\}\cdot \mathrm{<figure-callout\; id="0"\; label="l\; U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">l\; </figure-callout>}}$$

$$U_{}$$$${}_{0\mathit{rC}}=k_{11}\left(\mathit{j\omega }.1-\mathrm{<figure-callout\; id="0"\; label="l\; \cdot \; U"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">l\; </figure-callout>}\right)\cdot U_{}{}_{0\mathit{C}}\cdot e^{-j\mathrm{in\; the}\left\{\gamma \right\}\cdot \left(1-l\right)}+k_{12}\left(\mathit{j\omega }.1-l\right)\cdot I_{0C}\cdot e^{-j\mathrm{in\; the}\left\{\gamma \right\}\cdot \left(1-l\right)}$$

The pointers of the complex pointers related to the data window start are turned back to the error entry time.

mit: $$f\left(t_1\right)\mathit{Hüllkurve\; zum\; Zeitpunkt}{t}_1$$

$$f\left(t_2\right)\mathit{Hüllkurve\; zum\; Zeitpunkt}{t}_2$$

By means of high-pass filtering, the proportion of the fundamental can be eliminated. If this signal is subjected to RMS, a signal proportional to the envelope of the transient is produced. From this signal, the time constant of the decaying e-function can be determined by means of coefficient comparison: $$\tau =\frac{t_2-{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t</figure-callout>}}_1}{\ln \left(\frac{f\left(t_1\right)}{\mathrm{<figure-callout\; id="2"\; label="f\; t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}\left(t_{}\right)\left({}_2\right)}\right)}$$

With: $$\mathrm{<figure-callout\; id="1"\; label="f\; t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}\left(t_{}\right)\left({}_1\right)\mathit{Envelope\; at\; the\; time}{t}_1$$

$$\mathrm{<figure-callout\; id="2"\; label="f\; t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">f\; </figure-callout>}\left(t_{}\right)\left({}_2\right)\mathit{Envelope\; at\; the\; <figure-callout\; id="2"\; label="time\; t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">time\; </figure-callout>}{t}_{}{}_2$$

The FIG. 8 shows the spectra of zero current and zero voltage determined by an FFT (Fourier transform). From the spectrum of the voltage, the maximum value is searched in the range above the nominal frequency.

$$k=\mathit{inv}\left(\delta \cdot {\delta }^T\right)\cdot \delta$$

$$\mathrm{\Theta }=k\cdot I_0$$

mit $$I_0=\left(i_{0\left(1\right)}\cdots i_{0\left(N\right)}\right)$$

Taking advantage of the symmetry of the leakage effect, the center frequency can be determined from the voltage spectrum samples calculated by FFT by means of linear interpolation. With the now known signal parameters center frequency of the dominant harmonic fm and the decay time constant of the envelope, the following least squares estimator for the parameters of a signal model defined as follows can be established: $$\delta =\left(\begin{array}{ccc}\begin{array}{c}{e}^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t</figure-callout>}}_1}{\tau }}\cdot \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">sin</figure-callout>}\left(2\pi \cdot f_m\cdot t_1\right)\\ e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t</figure-callout>}}_1}{\tau }}\cdot \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">cos</figure-callout>}\left(2\pi \cdot f_m\cdot {\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\right)\\ \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">sin</figure-callout>}\left(2\pi \cdot f_m\cdot {\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t</figure-callout>}}_1\right)\\ \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">cos</figure-callout>}\left(2\pi \cdot f_m\cdot t_1\right)\\ e^{-\frac{{\mathrm{<figure-callout\; id="1"\; label="t"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t</figure-callout>}}_1}{\tau }}\end{array}& \cdots & \begin{array}{c}{e}^{-\frac{t_N}{\tau }}\cdot \mathrm{<figure-callout\; id="2"\; label="sin"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">sin</figure-callout>}\left(2\pi \cdot f_m\cdot t_N\right)\\ e^{-\frac{t_N}{\tau }}\cdot \mathrm{<figure-callout\; id="2"\; label="cos"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">cos</figure-callout>}\left(2\pi \cdot f_m\cdot {\mathrm{<figure-callout\; id="2"\; label="t\; N\; sin"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t\; </figure-callout>}}_N\right)& \\ \sin \left(2\pi \cdot f_m\cdot {\mathrm{<figure-callout\; id="2"\; label="t\; N\; cos"\; filenames="imgf0002.png,imgf0003.png"\; state="\{\{state\}\}">t\; </figure-callout>}}_N\right)& \\ \cos \left(2\pi \cdot f_m\cdot t_N\right)\\ e^{-\frac{t_N}{\tau }}\end{array}\end{array}\right)$$

$$k=\mathit{inv}\left(\delta \cdot {\delta }^T\right)\cdot \delta$$

$$\mathrm{\Theta }=k\cdot I_0$$

With $$I_0=\left({\mathrm{<figure-callout\; id="0"\; label="i"\; filenames="imgf0002.png,imgf0004.png"\; state="\{\{state\}\}">i</figure-callout>}}_{0\left(1\right)}\cdots i_{0\left(N\right)}\right)$$

The estimator calculates an optimal filter k. To calculate the zero or zero voltage complex pointer, it is sufficient to calculate the first two elements of the parameter vector. These elements represent the real and imaginary parts of the complex vector of the dominant equalizing vibration.

The Figures 9 and 10 show the approximation of the measured signal from zero voltage u0 and zero current i0 by the estimated signal u0est and i0est (formed from the signal model of the estimator using the estimated parameters) in each other's time resolution FIG. 9 the agreement of measured and estimated signals in the complete data window and the FIG. 10 the match of measured and estimated signals in the clipping.

The FIG. 11 shows the complex pointers formed from the parameters. In the FIG. 11 are clearly the size ratios between the fundamental wave pointers U50 and I50 and the hands Uos and Ios the dominant frequency fm of the transient response to recognize. The harmonic pointers Uos and Ios allow a much more reliable direction determination and fault location, since the magnitude of the current vector Ios is significantly greater than the basic current vector 150.

The FIG. 12 shows by way of example the cost function e (d) = (ΔUf) ² calculated with the pointers. The function shows the difference of the voltage at the fault location calculated with the complex phasors of the dominant transient frequency. For the error removal corresponding to the error, the error voltage calculated by both sides coincides and the cost function reaches its minimum. The minimum of the cost function can be calculated, for example, using the Matlab function "fmin-search". This function is based on the simplex algorithm. It can be seen that the error removal is at d = 0.04 (d = 39.86%).

A second exemplary embodiment for a ground fault detection will be described in more detail below.

The second embodiment exploits the transients arising in the event of a ground fault and calculates the zero and zero voltage complex phasors for this one-swing operation with an exponentially decaying envelope. For this purpose, the dominant natural frequency of the ground fault transient present in the zero voltage is used. From the phase of these complex pointers of zero current and zero voltage the earth fault direction is determined. Furthermore, the complex pointers determined in this way are transmitted via a communication device to the protective device, which protects the other end of the line to be monitored. For this purpose, an IP-based network technology can be used, which establishes a connection to the other substation briefly only when needed and terminated after a defined time.

The complex pointers of the two line ends are synchronized by means of pre-fault data or by detecting the entry time by a signal model for the signals in the faulty state to a common time base. From the complex pointers of the zero magnitudes, the percentage distance of the ground-fault location from one end of the line to the other is determined by solving the mesh equations FIG. 5 calculated. This solution can be done directly or using a non-linear optimization algorithm known per se.

The line data of the zero system required for solving the mesh equations are originally set with an estimate of the line data and automatically measured at an external ground fault and stored for later use. The solution of the mesh equation of the zero system can also be carried out with the 50Hz-pointers of the zero system quantities.

In each field device, with a rise in the zero voltage over an adjustable threshold value, a trigger signal is generated which triggers a recording of zero current and zero voltage of the outgoer connected to the field device. From this point on, a data window is selected and the signal spectrum of the zero voltage is determined by means of an FFT.

By determining the symmetry axis of the maximum value of the dominant harmonic in the spectrum, the frequency of the dominant harmonic is determined.

High-pass filtering separates the harmonic component of the transient from the fundamental and determines the rms value of the harmonic component. The decay time constant of the harmonic content is determined by coefficient comparison or by a least squares estimation method from the filtered RMS signal.

With the now known signal parameters transient frequency and decay time constant of the envelope, the complex pointer of the transient response is calculated by means of a least-squares estimator.

The absolute time of the fault entry and the complex pointer of the transient are transmitted alternately to the device at the other end of the line.

With the same direction indication of both line ends the error location after the already in connection with the FIGS. 1 to 14 calculated method.

If the direction is different, the quadripole parameters of the zero system are calculated and stored for use in a ground fault on the own line.

By determining the complex phasing of the transient, the line affected by the ground fault can also be detected with non-specially tuned transducers. So it can be made very low demands on the accuracy of the converter used.

Claims (15)

1. Method for producing a fault signal (F) which identifies the location of a ground fault on a line (60) between two line ends (A, C) wherein, in the method, the voltage and the current are measured at each of the two line ends, with measured values being formed, and, after or on detection of a ground fault, the location of the ground fault is determined,
   characterized in that

   - the harmonic component contained in the zero phase-sequence voltage or the zero phase-sequence current, as well as its decay time constant (τ) is determined for each of the two line ends, using the measured values,

   - the magnitude and phase of a harmonic vector measurement variable (U0A, I0A, U0C, I0C) are in each case formed using the harmonic component and the decay constant for each line end, wherein the time reference point of the phase of the harmonic vector measurement variable relates to the time of the ground fault detection at the respective line end,

   - the harmonic vector measurement variables formed in this way are rotated, starting from their respective line end, to a time in the past, and the time in the past and the point on the line at which the rotated-back harmonic vector measurement variables have at least approximately the same magnitude and at least approximately the same phase are determined,

   - and the location determined in this way is regarded as the location of the ground fault, and is output with the fault signal.
2. Method according to Claim 1,
   characterized in that

   - taking account of the telegraph equation, which describes the propagation of electromagnetic waves on lines, a first and a second zero phase-sequence voltage vector are calculated for a selectable point on the line, for a time which is located in the past corresponding to the propagation time to the selectable location, using the harmonic vector measurement variables of zero phase-sequence current and zero phase-sequence voltage at the two line ends, wherein the first zero phase-sequence voltage vector is calculated starting from the first line end in the direction of the second line end, and the second zero phase-sequence voltage vector is calculated starting from the second line end in the direction of the first line end,

   - the two zero phase-sequence voltage vectors calculated in this way are compared with one another, and that location is selected at which the calculated zero phase-sequence voltage vectors best match, and

   - the line location determined in this way is regarded as the location of the ground fault.
3. Method according to Claim 1 or 2,
   characterized in that

   - the magnitude and phase of the two harmonic vector measurement variables are in each case determined by means of an estimation method on the basis of a predetermined signal model, which models the time profile of the zero phase-sequence voltage in the case of a ground fault,

   - wherein the predetermined signal model takes account at least of the harmonic vector measurement variable to be determined at a defined vector angular frequency, the determined decay time constant of the harmonic component and a zero phase-sequence voltage vector measurement variable at the fundamental frequency of the zero phase-sequence voltage, and

   - wherein, during the course of the estimation method, the magnitude and the phase of the harmonic vector measurement variable are adapted such that the discrepancy between the time signal profile of the modeled signal of the signal model and the measured time signal profile of the measured values of the zero phase-sequence voltage is a minimum.
4. Method according to Claim 3, characterized in that a least squares estimation method, a Kalman filter algorithm or an ARMAX estimation method is used as the estimation method.
5. Method according to one of the preceding claims, characterized in that

   - a frequency which is dominant for the harmonic component is selected from the frequency spectrum of the harmonic component, and

   - the vector angular frequency of the two harmonic vector measurement variables is in each case defined such that it corresponds to the dominant frequency.
6. Method according to one of the preceding claims, characterized in that

   - that harmonic frequency whose amplitude is a maximum is determined in the harmonic component, and

   - the vector angular frequency of the two harmonic vector measurement variables is in each case defined such that it corresponds to this harmonic frequency.
7. Method according to one of the preceding claims, characterized in that
   the time window for the data used to determine the harmonic vector measurement variables is determined such that the time window start is fixed at the start of the rise of the zero phase-sequence voltage after a predetermined threshold value has been exceeded.
8. Method according to one of the preceding claims, characterized in that
   the harmonic component is determined in that

   - a measurement window for which the frequency spectrum of the zero phase-sequence voltage is determined by means of a Fourier transformation is in each case opened for each line end after the detection of the ground fault, and

   - the frequency spectrum is subjected to high-pass filtering, in which the harmonics of the fundamental frequency of the zero phase-sequence voltage are separated, forming the harmonic component.
9. Method according to one of the preceding claims, characterized in that
   the decay constant is determined in that

   - the root mean square value of the harmonic component is determined and the decay time constant of the root mean square value is determined, and

   - the determined decay time constant of the root mean square value is regarded as the decay time constant of the harmonic component.
10. Method according to one of the preceding claims, characterized in that
    the measurement of the voltage at the two line ends is carried out free of synchronization, and the voltage measured values at the two line ends are unsynchronized.
11. Arrangement for producing a fault signal, which identifies the location of a ground fault on a line (60) between a first and a second line end (A, C), wherein the arrangement has:

    - a first measurement instrument (40) at the first line end (A) of the line,

    - a second measurement instrument (42) at the second line end (C) of the line, and

    - an evaluation device (200), which is connected to the two measurement instruments and is suitable for using the measured values from the two measurement instruments to carry out a method according to one of the preceding Claims 1-10.
12. Arrangement according to Claim 11,
    characterized in that
    the evaluation device is formed by a programmed data processing installation.
13. Arrangement according to Claim 11 or 12,
    characterized in that
    the evaluation device is arranged in a central device to which the two measurement instruments are connected.
14. Arrangement according to Claim 11 or 12,
    characterized in that

    - the two measurement instruments are connected to one another and

    - the evaluation device is implemented in one of the measurement instruments.
15. Field device (42), in particular a protective device, for connection to one line end (C) of an electrical line (60) and for identification of a ground fault on the line, having

    - an evaluation device (200) which is suitable for carrying out a method according to one of the preceding Claims 1-10, and

    - a data connection (D42) for connection to another measurement instrument (40) for receiving measured values (U0A, I0A) which relate to the other line end of the line.

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